To characterize the performance upper bound of the IRS-aided WPCN system via joint dynamic beamforming design and resource allocation, it is assumed that the CSI of all channels involved is perfectly known at the HAP, based on the various channel acquisition methods discussed in [1]}. Signalling overhead and incomplete CSI will result in performance loss and the study of their impacts on the system performance is beyond the scope of this paper. The equivalent baseband channels from the HAP to the IRS, from the IRS to device \(k\) , and from the HAP to device \(k\)  are denoted by \(\mathbf {g}\in \mathbb {C}^{N\times 1}\) , \(\mathbf {h}^H_{r,k}\in \mathbb {C}^{1\times N}\) , and \({h}^H_{d,k}\in \mathbb {C}\) , respectively, where \(k = 1, \cdots ,K\) .
